The reception and the demodulation of radio signals can be performed by means of conventional reception concepts, which are based on the principle of heterodyne reception with subsequent digital quadrature mixing. However, more advanced reception concepts, in which directly mixing methods are used, are becoming increasingly preferred for reasons relating to lower power consumption and the avoidance of chip-external filters for mirror-image frequency suppression. In the case of directly mixing receiver concepts, the radio signal, which is received via an antenna and is amplified, is split into an inphase (I) and a quadrature (Q) path and is mixed in both paths using the output frequency from a local oscillator, the oscillator frequencies which are supplied to the mixers being mutually shifted through 90° by means of a phase shifter. Consequently, with this reception concept, the quadrature demodulation is executed to recover the information-carrying baseband signals in analogue circuit engineering.
It is possible to make use in radio transmitters of, for example, quadrature modulation in the form of quadrature amplitude modulation (QAM) or of quadrature phase modulation (QPSK, Quadrature Phase Shift Keying), a carrier oscillation always being split into mutually orthogonal I and Q components, and both components being modulated by independent data sequences, and the modulated signals being combined to form an output signal to be transmitted.
So-called IQ asymmetries or IQ distortions, that is to say asymmetries in amplitude and phase, occur between the quadrature components as a result of technically induced inaccuracies in the production process and of the non-ideal natures of the analogue mixers and oscillators, as well as of deviations between the filters in the I and Q paths. Real and imaginary parts of the complex baseband signal are not mutually phase-shifted by exactly 90° and, moreover, deviations in amplitude occur between the I and Q paths. These IQ asymmetries have a negative influence on the reception quality of a radio signal receiver with an analogue quadrature stage (also denoted as a complex radio signal receiver). For example, in the case of OFDM-based transmission systems, for example, the IQ asymmetries lead in the frequency domain, that is to say after the so-called FFT transformation (fast Fourier transform) in the receiver, to mutual interference between in each case two data symbols on the subcarriers whose frequencies are arranged symmetrically relative to the centre frequency of the OFDM frequency spectrum. Owing to the IQ asymmetry added in the time domain, each data symbol transmitted on a subcarrier n generates a signal contribution on a subcarrier with the index −n (mirror-image frequency). The superimposition therefore leads to distortions in the useful signals at the positions n and −n. In the dissertation entitled “Verfahren der digitalen Kompensation von Unsymmetrien der analogen Quadraturmischung in OFDM-Empfängern” [Method for the digital compensation of asymmetries in analogue quadrature mixing in OFDM receivers”] by Andreas Schuchert, accepted by the Department of Electrical Engineering and Information Technology of Wuppertal Mining University) Chapter 4 gives a mathematical description of the IQ asymmetries, and supplies a quantitative estimate of the interference contribution occurring at the mirror-image frequency of a desired signal.
The said IQ asymmetries also have a negative effect in just such a way on the quality of the radio transmitters operating with the quadrature modulation method.
U.S. Pat. No. 5,705,949 describes a compensation method of IQ asymmetries in a complex radio signal receiver by means of which the asymmetries between the I path and the Q path are compensated with regard to the offset, the signal level and the phase in a digital signal processor (DSP). With regard to the phase compensation, the phase error between the components is firstly determined, and subsequently a compensation matrix is calculated in the DSP and multiplied by the vector of the I and Q components in order to obtain the compensated I and Q components. The phase compensator has the task of reversing the IQ distortion caused by the phase error Δφ in accordance with the following equation.
                              [                                                                      S                  I                                                                                                      S                  Q                                                              ]                =                              [                                                                                cos                    ⁡                                          (                                                                        Δ                          ⁢                                                                                                          ⁢                          φ                                                2                                            )                                                                                                            sin                    ⁡                                          (                                                                        Δ                          ⁢                                                                                                          ⁢                          φ                                                2                                            )                                                                                                                                        sin                    ⁡                                          (                                                                        Δ                          ⁢                                                                                                          ⁢                          φ                                                2                                            )                                                                                                            cos                    ⁡                                          (                                                                        Δ                          ⁢                                                                                                          ⁢                          φ                                                2                                            )                                                                                            ]                    ·                      [                                                                                S                    I                    ′                                                                                                                    S                    Q                    ′                                                                        ]                                              (        1        )            
Here, the primed variables are the undistorted IQ components while the unprimed variables represent the IQ components distorted by the phase error.
To reverse the phase distortion, the compensation matrix which is inverse to the distortion matrix of the equation (1) and appears as follows except for a constant factor:
                    [                                                            cos                ⁡                                  (                                                            Δ                      ⁢                                                                                          ⁢                      φ                                        2                                    )                                                                                    -                                  sin                  ⁡                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                        φ                                            2                                        )                                                                                                                          -                                  sin                  ⁡                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                        φ                                            2                                        )                                                                                                      cos                ⁡                                  (                                                            Δ                      ⁢                                                                                          ⁢                      φ                                        2                                    )                                                                    ]                            (        2        )            can be multiplied by both sides of the equation.
Consequently, the conversion of this compensation matrix into a phase compensation circuit requires four multipliers and two adders using digital circuit engineering, as represented in the phase compensation part of the digital signal processor shown in the sole figure of the drawing in U.S. Pat. No. 5,705,949.
A comparable compensation scheme for a QPSK modulation method (quadrature phase shift keying) is used in EP 1 120 944 A2. The modulation scheme of FIG. 1 in that document includes for the compensation of the IQ phase errors an IQ phase rotator which is illustrated in FIG. 7 of that document. In this case, as well, four digital multipliers and two digital adders are used to carry out the multiplication by the compensation matrix in accordance with the above compensation matrix (2).
There is a relatively high outlay on the implementation of the phase compensation scheme of the two said documents, since, firstly, four digital multipliers have to be used, and two different correction signals must be fed to these multipliers, specifically the sine and the cosine of half the phase error. The two correction signals of sine and cosine must therefore be quantized, and the values must be stored in a table or must be calculated with the aid of a non-linear function of the uniform control signal Δφ. In order, furthermore, to be able to represent the cosine with sufficient resolution, a relatively large word length is required, in particular, for small values of Δφ, for which the cosine is close to 1, and the two multipliers which are fed the cosine therefore have to be of relatively large design.